| Abstract: |
| In this paper, we study the $\mathcal{L}^p$ convergence rate of the numerical approximation to the solution of the McKean-Vlasov stochastic differential equations (MV-SDEs) with super-linear growth in the spatial component in the drift. In contrast to standard SDEs, MV-SDEs require an approximation of the distribution law, and here we adopt the stochastic particle method to approximate the true measure using the empirical measure, the time-stepping scheme adopted here is the tamed Euler method. First, we show the strong convergence rate of the propagation of chaos (PoC) is of order $O(N^{-1/{2}})$ under the $\mathcal{L}^p$-norm for any $p\ge 2$, where N is the number of weakly interacting particles. This order is not only better than the existing results, but it is also across dimensions. In the second part we prove that the tamed Euler method is strongly convergent with the order of $O(\Delta^{1/2})$, which is consistent with the classical results. Finally, we present numerical experiments which confirm our theoretical estimates. |
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